Note on the Fenchel transform in the Heisenberg group |
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| Authors: | A Calogero |
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| Institution: | a Dipartimento di Statistica, Università degli Studi di Milano Bicocca, Via Bicocca degli Arcimboldi 8, I-20126 Milano, Italy
b Dipartimento di Metodi Quantitativi per le Scienze Economiche ed Aziendali, Università degli Studi di Milano Bicocca, Via Bicocca degli Arcimboldi 8, I-20126 Milano, Italy |
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| Abstract: | Given a real-valued function defined on the Heisenberg group H, we provide a definition of abstract convexity and Fenchel transform in H, that takes into account the sub-Riemannian structure of the group. In our main result, we prove that, likewise the classical case, a convex function can be characterized via its iterated Fenchel transform; the properties of the H-subdifferential play a crucial role. |
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| Keywords: | Heisenberg group Convexity Subdifferentiability Fenchel transform Abstract convexity |
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